I came across the following Lemma in Mitsuyasu Hashimoto's Equivariant Twisted Inverses; it is Lemma 11.2 on page 107 of this pdf.
Let $\mathcal{A}$ be an abelian category which satisfies the (AB3) ...

The proof of statements either uses Galois theory or Artin primitive element theorem.I would like to know whether there is a proof without using these.The reason to avoid using Galois theory is that ...

Consider the category with the standard Lebesgue measure space $\Omega$ as its only object and measure type preserving nonincreasing (equivalence classes of) maps as morphisms.
Question: is there an ...

Convention:
Before I start, please note that it is not going to be sufficient to assume that the topology is subcanonical or that the site $C$ has finite limits, since the application I have in mind ...

Let $A$ be a small category, and let $X:=Psh(A)$ denote the category of presheaves on $A$. It is a theorem that for any such category $X$, there exists a small set $M$ of monomorphisms admitting the ...